We calculate the tunneling magnetoresistance (TMR) of Fe/ZnSe/Fe/ZnSe/Fe (001) double magnetic tunnel junctions (DMTJs) as a function of the in-between Fe layer's thickness, and compare these results with those of Fe/ZnSe/Fe simple junctions. The electronic band structures are modeled by a parametrized tight-binding Hamiltonian fitted to ab initio calculations, and the conductance is calculated in the coherent, elastic and linear response regime within the Landauer formalism. We find that the DMTJs' TMR values can be higher than those of simple junctions, and that the TMR enhancements are mainly due to a decrease in the conductance of all but one spin channel and not due to the spin-dependent resonant tunneling effect. For a wide ZnSe width range, the TMR enhancements are large and practically independent of the in-between Fe thickness, which may be relevant for applications in spintronics.